Problem: A total of 17 teams play in a single-elimination tournament.  (A single-elimination tournament is one where once a team has lost, it is removed from the competition.)  How many total games must be played before a winner can be declared, assuming there is no possibility of ties?
Each game played removes one team from the tournament.  Since we seek to remove 16 teams from the tournament, we must play $\boxed{16}$ games.